Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

We construct counterexamples to some conjectures of J. Birman and R. F. Williams concerning the knotting and linking of closed orbits of flows on 3-manifolds. By establishing the existence of "universal templates," we produce examples of flows on $S^3$ containing closed orbits of all knot and link types simultaneously. In particular, the set of closed orbits of any flow transverse to a fibration of the complement of the figure-eight knot in $S^3$ over $S^1$ contains representatives of every (tame) knot and link isotopy class. Our methods involve semiflows on branched 2- manifolds, or {\em templates}.

Copyright American Mathematical Society 1995

TeX source (27K)
DVI (26.5K)
PostScript (235.1K)

Article Info

• ERA Amer. Math. Soc. 01 (1995), pp. 91-97
• Publisher Identifier: S1079-6762-95-02006-X
• 1991 Mathematics Subject Classification. Primary 57M25, 58F22; Secondary 58F25, 34C35.
• Key words and phrases. Knots, links, branched 2-manifolds, flows.
• Received by the editors June 16, 1995
• Communicated by Krystyna Kuperberg
• Comments (When Available)

Robert W. Ghrist

Center for Applied Mathematics, Cornell University, Ithaca NY, 14853

Current address: Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544; Institute for Advanced Study, Princeton, NJ 08540.

E-mail address: rwghrist@math.princeton.edu; robg@math.ias.edu

The author was supported in part by an NSF Graduate Research Fellowship.

The author wishes to thank Philip Holmes for his encouragement and support.